Conditional similarity reductions of the (2 + 1)-dimensional KdV equation via the extended Lie group approach

Xiao Yan Tang; Xian Min Qian; Ji Lin; S. Y. Lou

doi:10.1143/JPSJ.73.1464

Conditional similarity reductions of the (2 + 1)-dimensional KdV equation via the extended Lie group approach

Xiao Yan Tang
, Xian Min Qian
, Ji Lin
, S. Y. Lou^*

^*Corresponding author for this work

Shanghai Jiao Tong University
CAS - Institute of Computational Mathematics and Scientific-Engineering Computing
Shaoxing University
Zhejiang Normal University
University of New South Wales

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

The classical and nonclassical Lie group approaches are extended and applied to construct new conditional similarity reductions for nonlinear systems. The application of the method to a simple (2 + 1)-dimensional KdV equation results in not only the known conditional similarity reductions obtained by the modified Clarkson and Kruskal's direct method but also a great diversity of classical and nonclassical conditional similarity reductions.

Original language	English
Pages (from-to)	1464-1475
Number of pages	12
Journal	Journal of the Physical Society of Japan
Volume	73
Issue number	6
DOIs	https://doi.org/10.1143/JPSJ.73.1464
State	Published - Jun 2004
Externally published	Yes

Keywords

(2 + 1)-dimensional KdV equation
Conditional similarity reduction
Conditional symmetry
The extended Lie group approach

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10.1143/JPSJ.73.1464

Cite this

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abstract = "The classical and nonclassical Lie group approaches are extended and applied to construct new conditional similarity reductions for nonlinear systems. The application of the method to a simple (2 + 1)-dimensional KdV equation results in not only the known conditional similarity reductions obtained by the modified Clarkson and Kruskal's direct method but also a great diversity of classical and nonclassical conditional similarity reductions.",

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AU - Lou, S. Y.

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AB - The classical and nonclassical Lie group approaches are extended and applied to construct new conditional similarity reductions for nonlinear systems. The application of the method to a simple (2 + 1)-dimensional KdV equation results in not only the known conditional similarity reductions obtained by the modified Clarkson and Kruskal's direct method but also a great diversity of classical and nonclassical conditional similarity reductions.

KW - (2 + 1)-dimensional KdV equation

KW - Conditional similarity reduction

KW - Conditional symmetry

KW - The extended Lie group approach

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Conditional similarity reductions of the (2 + 1)-dimensional KdV equation via the extended Lie group approach

Abstract

Keywords

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